A Generalization of Gröbner Basis Algorithms to Polycyclic Group Rings

Autor:	Birgit Reinert, Klaus Madlener
Rok vydání:	1998
Předmět:	Algebra Gröbner basis Computational Mathematics Algebra and Number Theory Membership problem Fractional ideal Polycyclic group Decision problem Decidability Mathematics Group ring
Zdroj:	Journal of Symbolic Computation. 25(1):23-43
ISSN:	0747-7171
DOI:	10.1006/jsco.1997.0165
Popis:	It is well-known that for the integral group ring of a polycyclic group several decision problems are decidable, in particular the ideal membership problem. In this paper we define an effective reduction relation for group rings over polycyclic groups. This reduction is based on left multiplication and hence corresponds to left ideals. Using this reduction we present a generalization of Buchberger's Gröbner basis method by giving an appropriate definition of “Gröbner bases” in this setting and by characterizing them using the concepts of saturation and s-polynomials. The approach is extended to two-sided ideals and a discussion on a Gröbner bases approach for right ideals is included.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e15e1a1dcaf757ddf99c71b9b8b61186 Zobrazit plný text záznamu Full Text from ScienceDirect